Detection of Scattered Light from the Hot Dust in HD 172555?,?? N

A&A 618, A151 (2018) Astronomy https://doi.org/10.1051/0004-6361/201832674 & © ESO 2018 Astrophysics

Detection of scattered light from the hot dust in HD 172555?,?? N. Engler1, H. M. Schmid1, S. P. Quanz1, H. Avenhaus2, and A. Bazzon1

1 Institute for Particle Physics and Astrophysics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland e-mail: [email protected] 2 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany

Received 19 January 2018 / Accepted 23 July 2018

ABSTRACT

Context. Debris disks or belts are important signposts for the presence of colliding planetesimals and, therefore, for ongoing planet formation and evolution processes in young planetary systems. Imaging of debris material at small separations from the star is very challenging but provides valuable insights into the spatial distribution of the so-called hot dust produced by solid bodies located in or near the habitable zone. We report the first detection of scattered light from the hot dust around the nearby (d = 28.33 pc) A star HD 172555. Aims. We want to constrain the geometric structure of the detected debris disk using polarimetric differential imaging (PDI) with a spatial resolution of 25 mas and an inner working angle of about 0.100. Methods. We measured the polarized light of HD 172555, with SPHERE/ZIMPOL, in the very broadband (VBB) or RI filter (λc = 735 nm, ∆λ = 290 nm) for the projected separations between 0.0800 (2.3 au) and 0.7700 (22 au). We constrained the disk parameters by fitting models for scattering of an optically thin dust disk taking the limited spatial resolution and coronagraphic attenuation of our data into account. Results. The geometric structure of the disk in polarized light shows roughly the same orientation and outer extent as obtained from thermal emission at 18 µm. Our image indicates the presence of a strongly inclined (i ≈ 103.5◦), roughly axisymmetric dust belt with an outer radius in the range between 0.300 (8.5 au) and 0.400 (11.3 au). An inner disk edge is not detected in the data. We derive a lower −5 limit for the polarized flux contrast ratio for the disk of (Fpol)disk/F∗ > (6.2 ± 0.6) × 10 in the VBB filter. This ratio is small, only ∼9%, when compared to the fractional infrared flux excess (≈ 7.2 × 10−4). The model simulations show that more polarized light could be produced by the dust located inside ≈2 au, which cannot be detected with the instrument configuration used. Conclusions. Our data confirm previous infrared imaging and provide a higher resolution map of the system, which could be further improved with future observations. Key words. planetary systems – scattering – stars: individual: HD 172555 – techniques: high angular resolution – techniques: polarimetric

1. Introduction Moerchen et al. 2010; Schneider et al. 2014; Choquet et al. 2016; Olofsson et al. 2016; Bonnefoy et al. 2017). Young stars are often surrounded by circumstellar dust In the absence of imaging data, the location of the bulk debris disks or rings. These consist of solid bodies, such as of dust in the system can be inferred from the grain tempera- planetesimals and comets, as well as large amounts of dust ture derived by SED modeling. Based on modeling results, most and small amounts of gas. Small dust grains with a broad size debris disks have been found to harbor warm dust, meaning that distribution are generated in steady collisions of solid bodies the temperature of small grains lies between 100 K and approxi- and perhaps by the evaporation of comets. Debris disks are mately 300 K (e.g., Moór et al. 2006; Trilling et al. 2008; Chen usually recognized by infrared (IR) excess on top of the spectral et al. 2011; Morales et al. 2011). Cold debris reside far away from energy distribution (SED) of the stellar photosphere because the host star where their temperature does not exceed 100 K. The of the thermal emission of the heated dust grains (see, e.g., prominent analogs to warm and cold dust belts are the main aster- Wyatt 2008; Matthews et al. 2014, for a review). In scattered oid belt at 2–3.5 au and the Kuiper belt between 30 and 48 au in > 3 light, debris disks are usually very faint, i.e., 10 times fainter the solar system (Wyatt 2008). Aside from this, several stars with than the host star, and therefore they are difﬁcult to image. To hot disks have been found (Wyatt et al. 2007a; Fujiwara et al. date, several dozen debris disks have been spatially resolved 2009) based on the IR excess with an estimate temperature above in various wavelength bands, from visible to millimeter, using 300 K. The stars that possess hot dust are very interesting tar- various space and ground-based telescopes. These data provide gets because the submicrometer-sized grains at a small distance important constraints on the debris disk morphologies (e.g., from a star could be a signpost for transient collision events. HD 172555 (HIP 92024, HR 7012) is one of the most studied objects ? Based on data collected at the European Southern Observatory, Chile among these special stellar systems (Cote 1987; Schütz et al. under program 095.C-192. 2005; Chen et al. 2006; Wyatt et al. 2007b; Lisse et al. 2009; ?? The reduced images (FITS ﬁles) are available at the CDS via Quanz et al. 2011; Smith et al. 2012; Riviere-Marichalar et al. anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via 2012; Johnson et al. 2012; Kiefer et al. 2014; Wilson et al. 2016; http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/618/A151 Grady et al. 2018).

Article published by EDP Sciences A151, page 1 of 15 A&A 618, A151 (2018)

HD 172555 is a V = 4.8m, A7V star (Høg et al. 2000; Gray the SPHERE (Spectro-Polarimetric High-contrast Exoplanet et al. 2006) at a distance of 28.33 ± 0.19 pc (Gaia Collaboration REsearch) instrument. The SPHERE instrument was developed 2016) and a member of the β Pictoris moving group. The deduced for high-contrast observations in the visual and near-IR spectral age for the group is 23 ± 3 Myr (Mamajek & Bell 2014). HD range and includes an extreme adaptive optics (AO) system and 172555 has a K5Ve low mass companion CD-64 1208, separated three focal plane instruments for differential imaging (Dohlen by more than 2000 au or 71.400 (Torres et al. 2006). The Infrared et al. 2006; Beuzit et al. 2008; Kasper et al. 2012; Fusco et al. Astronomical Satellite (IRAS) identified HD 172555 as a Vega- 2014; Schmid et al. 2018). like star that has a large IR excess with an effective temperature The ZIMPOL polarimetry is based on a modulation– of 290 K (Cote 1987). Mid-infrared (mid-IR) spectroscopy from demodulation technique and our observations of HD 172555 the ground (Schütz et al. 2005) and 5.5–35 µm spectroscopy in the very broadband (VBB) filter were carried out in the obtained with the Spitzer Infrared Spectrograph (IRS) show very fast modulation mode using field stabilization, which is also pronounced SiO features (Chen et al. 2006, their Fig.2d) indicat- known as the P2 derotator mode. The ZIMPOL modula- ing large amounts of submicron sized crystalline silicate grains tion technique measures the opposite polarization states of with high temperatures (>300 K). Lisse et al.(2009) proposed, incoming light quasi-simultaneously and with the same pixels based on the spectral analysis of mineral features, that the IR- such that differential aberrations between I⊥ and Ik are mini- excess emission originates from a giant collision of large rocky mized. Fast modulation means a polarimetric cycle frequency planetesimals similar to the event that could have created the of 967.5 Hz, which is obtained with a ferro-electric liquid Earth–Moon system. crystal (FLC) and a polarization beam splitter in front of Until now, only one resolved image of the HD 172555 debris the demodulating CCD detector. The high detector gain of − disk existed that was obtained in the Qa band (λc = 18.30 µm, 10.5 e /ADU allows broadband observations with high photon ∆λ = 1.52 µm; hereafter Q band) with the Thermal-Region rates without pixel saturation and ensures high sensitivity at Camera Spectrograph (TReCS) at Gemini South telescope and small angular separations at the expense of a relative high read- described by Smith et al.(2012). They detected extended emis- out noise. The ZIMPOL VBB or RI filter used (λc = 735 nm, sion after subtraction of a standard star point spread function ∆λ = 290 nm) covers the R band and I band. Polarimetric data (PSF), which is consistent with an inclined disk with an ori- were taken in coronagraphic mode using the Lyot coronagraph entation of the major axis of θ = 120◦, an inclination of ≈75◦, V_CLC_MT_WF with a diameter of 155 mas. The mask is semi- and a disk outer radius of 8 au. In Si-5 filter (λc = 11.66 µm, transparent such that the central star is visible as faint PSF in the ∆λ = 1.13 µm; hereafter N band) data, the disk was not detected. middle of attenuation region if the stellar PSF is of good quality Combining these results with the visibility functions measured (good AO corrections) and well centered on the mask. Short with the MID-infrared Interferometric instrument (MIDI), Smith flux calibrations (the star was offset from the coronagraphic et al.(2012) concluded that the warm dust radiating at ∼10 µm mask) with detector integration time (DIT) of 1.2 s and total is located inside 8 au from the star or inside the detected 18 µm exposure time of 14.4 s were also taken in each run using the emission. neutral density filter ND2 with a transmission of about 0.87% The proximity of the host star and strong excess in the mid- for the VBB filter to avoid heavy saturation of the PSF peak. −4 IR (LIR/L∗ = 7.2 × 10 ; Mittal et al. 2015) from hot dust, makes The ZIMPOL instrument is equipped with two detec- HD 172555 an excellent, yet challenging, object for the search tors/cameras, cam1 and cam2, which both have essentially the of scattered light. In this paper, we report the first detection of same field of view of 3.600 × 3.600. The format of the processed scattered light from the hot debris disk around HD 172555 with frame is 1024 × 1024 pixels, where one pixel corresponds to polarimetric differential imaging (PDI). 3.6 × 3.6 mas on sky. The spatial resolution of our data provided We present the PDI data from 2015 taken with the Zurich by the AO system is about 25 mas. IMaging POLarimeter (ZIMPOL; Schmid et al. 2018) at the The HD 172555 data were taken at three different sky ori- Very Large Telescope (VLT) in Chile. The ZIMPOL instrument entations on the CCD detectors with position angle (PA) offsets provides high-contrast imaging polarimetry, coronagraphy of 0◦, 60◦, and 120◦ with respect to sky north. For each field with a small inner working angle of ∼0.100, and high spatial orientation, eight polarimetric QU cycles were recorded con- resolution of ∼25 mas. The next section presents the available sisting each of four consecutive exposures of the Stokes linear data together with a brief description of the instrument. polarization parameters +Q, −Q, +U, and −U using half-wave Section3 describes the data reduction and Sect.4 the obtained plate (HWP) offset angles of 0◦, 45◦, 22.5◦, and 67.5◦, respec- results. Section5 includes analysis of the observed disk tively. For each exposure, eight frames with DIT of 10 s were morphology and photometry. For the interpretation of the taken and this yields a total integration of 10 s × 8 frames × data, we calculated three-dimensional (3D) disk models for 4 exposures × 8 cycles or ∼42.7 min. Because of a timing error spatial distribution of dust to put constraints on the geometric in the control law (see Maire et al. 2016) of the derotator during parameters of the disk and to estimate the flux cancellation the first three runs performed in June 2015, the program was re- effects in the Stokes Q and U parameters. In Sect.6, we compare executed in August and September 2015. However, it turned out our results with previous TReCS and MIDI observations (Smith that this timing error was so small that it does not significantly et al. 2012). We also investigate the possible presence of a affect the imaging of an extended source at small separation. very compact dust scattering component that would not be Therefore, none of the six disk observations for HD 172555 are detectable in our data. We conclude and summarize our findings degraded by this effect. All our deep polarimetric observations in Sect.7. of HD 172555 are listed in Table1 together with the observing conditions, which have an important impact on the data quality. 2. Observations 3. Data reduction Observations of HD 172555 were taken in service or queue mode during six runs in 2015 as part of the open time The data were reduced with the SPHERE/ZIMPOL data reduc- program 095.C-192 using ZIMPOL, the visual subsystem of tion pipeline developed at ETH Zurich. We applied very similar

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Table 1. Log of observations with the atmospheric conditions for each run.

Date Observation Field Observing conditions (on average) identiﬁcationa offset (◦) Airmass Seeing (00) Coherence time (ms) Wind speed (m s−1) 2015-06-21 OBS172_0004-0036 0 1.32 1.39 1.1 7.9 2015-06-26 OBS177_0010-0042 120 1.31 0.78 3.5 6.7 2015-07-12 OBS193_0049-0081 60 1.33 1.41 0.9 1.8 2015-09-06 OBS249_0028-0060 0 1.35 0.93 3.8 9.0 2015-09-06 OBS249_0061-0094 60 1.47 1.11 3.4 8.7 2015-09-07 OBS250_0002-0034 120 1.55 2.01 1.0 16.1

Notes. (a)The observation identification corresponds to the fits-file header keyword “origname” without prefix “SPHERE_ZIMPOL_”. The first three digits give the day of the year followed by the four-digit observation number. Instrument setup for the deep imaging mode: fast polarimetry, VBB filter, derotator mode P2, coronagraph V_CLC_MT_WF, and total exposure time for each run 42.7 min. Instrument setup for the flux calibration mode: fast polarimetry, VBB filter, density filter ND2, derotator mode P2, and total exposure time for each run 14.4 s. procedures as in Engler et al.(2017) using flux normalization The quality of the data can be easily recognized in the coron- before polarimetric combination of the data. agraphic intensity images. These images show, for the best night For high-contrast polarimetry at small separations from the (top), a much weaker halo and a weaker speckle ring at a separa- star, an accurate centering and the correction of the ZIMPOL tion of about r ≈ 0.3500 than for the second best night (middle). polarimetric beam-shift are important (Schmid et al. 2018). The For all other nights, the disturbing light halo and speckles from stellar position behind the mask should be determined with a the central star are even stronger (see Fig. B.1). Also clearly vis- precision higher than 0.3 pixels, otherwise the final image shows ible in Fig.1 is the rotated speckle pattern in the top I image, strong offset residuals disturbing the detection of a faint polari- which was taken with a field orientation of 120◦, with respect to metric signal. For the fine centering, we fitted a 2D Gaussian the middle I image taken without field orientation offset or 0◦. function using a central subimage with a radius of eight pixels In the latter image, two strong quasi-static speckles from the AO containing the stellar light spot transmitted through a semitrans- system (indicated with white arrows) are located left and right parent coronagraphic focal plane mask. from the central source on the speckle ring. The same speckles The output of the data reduction pipeline consists of images are rotated in the top image by 120◦ because of the applied field of the intensity or Stokes I and the Stokes Q and U fluxes, where rotation. Q = I0 − I90 is positive for a linear polarization in N–S direc- The Qϕ image from the best night in the top row shows a pos- tion and U = I45 − I135 is positive for a polarization in NE–SW itive signal or tangential polarization for regions just ESE and direction. For the data analysis, we transformed the Q and U WNW from the coronagraphic mask and some noisy features at images into a tangential or azimuthal polarization images Qϕ and the location of the two strong speckles. The corresponding Uϕ Uϕ, locally defined with respect to the central light source. This image is also noisy but shows no predominant extended feature transformation is useful for an optically thin circumstellar scat- as seen in Qϕ. The same ESE–WNW extension is also present tering region because the polarization signal is mainly in the Qϕ in the Qϕ image of the second best night, but now the disturbing component, while Uϕ should be zero (e.g., Schmid et al. 2006; strong speckles are adding noise in the E–W direction, particu- see also AppendixA). larly well visible in the Uϕ image. Besides this, both Qϕ and Uϕ During the data reduction, it turned out that an accurate cen- for the second best night show a quadrant pattern that is typi- tering of our HD 172555 images is difficult and not possible for a cal for a not perfectly corrected component from the telescope substantial portion of our data because several runs suffered from polarization. The following analysis of the disk morphology and 00 mediocre atmospheric conditions with a seeing >1 and there- modeling are based on the Qϕ image in the top row obtained fore strongly reduced AO performance. Because of this problem under the best observing conditions because these data are the only data from the best night 177 (2015-06-26; see Table1) with least affected by noise. an average seeing of 0.7800 and most data from the second best The fact that we see the same kind of extended feature in the night 249 (2015-09-06) with seeing of 0.9300 could be used for ESE-WNW orientation in both data sets (from the best and sec- our high-contrast polarimetry. Figure B.1 shows the Stokes I, Q, ond best nights), while other features can clearly be associated and U images of these data sets in comparison with the reduced with instrumental effects, strongly supports an interpretation that data from the other observing runs that were affected by poor this is a real detection of the debris dust around HD 172555. This observing conditions. is further supported by the fact that the orientation and extent To have a higher S/N per resolution element, images were of the detected feature coincides at least roughly with the disk 8 × 8 (Fig.1) binned for the data analysis and modeling. In detection reported previously by Smith et al.(2012) based on Fig.2 we used a smaller binning ( 6 × 6) to preserve the spatial imaging in the mid-IR. information and to have a more detailed picture of the disk. In our image there is a prominent bright spot located below the coronagraphic mask. Most likely it is a spurious feature orig- 4. Features in the reduced data inating from image jitter and the temporal leakage of light of the central star from behind the coronagraphic mask. It is seen more The top row of Fig.1 shows the main results of our data reduc- particularly in 177 data set, which argues against this being a real tion, i.e., the mean intensity or Stokes I, Stokes Qϕ, and Uϕ feature. images using all eight cycles of the best night. The second row A final remark on the data quality. Our data look noisy and shows the same for six out of eight cycles from the second best are affected by not well corrected instrumental effects. How- night. The bottom row is the mean of these data. ever, we note that the signals in the Qϕ and Uϕ images are at

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14 au

Fig. 1. Polarimetric differential imaging data of HD 172555 with the VBB filter (590–880 nm). The 8 × 8 binned images show polarized flux computed as Stokes I (left column), Qϕ (middle column), and Uϕ (right column) parameters. Top row: observation OBS177_0010-0042 (see Table1 for the observational conditions) data averaged over 8 QU cycles. Middle row: observation OBS249_0028-0060 data averaged over 6 QU cycles. Bottom row: average of the data presented in the top and middle rows. The position of the star is denoted by a yellow asterisk. White arrows point out quasi-static speckles from the AO system. In all images north is up and east is to the left. The color bars show the counts per binned pixel. a very low level of 0.001 of the signal in the intensity frame 5. Analysis −5 or the surface brightness in the Qϕ image is on the order 10 of the expected peak flux of the central star for a separation 5.1. Disk position angle and morphology of <0.3 arcsec. The detection of this faint target requires very To determine the PA of the disk θdisk, we varied the position of ◦ ◦ high-contrast polarimetry at small angular separation. Not all the disk major axis in the range from θdisk = 105 to θdisk = 125 ◦ instrumental effects are understood and can be calibrated at this with a step of 0.5 . Each time the Qϕ image was rotated by ◦ level of sensitivity yet. θdisk − 90 clockwise to place the disk major axis horizontally

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y N b E A B

0.2 ’’ 6 AU

Fig. 2. Qϕ image (panel a) and isophotal contours of polarized light intensity overlying the Qϕ image (panel b). The original data (OBS177_0010- 0042) were 6 × 6 binned to highlight the disk shape and to reduce the photon noise level. The position of the star is indicated by a yellow asterisk. White brackets in the top panel show the boundaries of two rectangular areas where the counts were summed up to retrieve the total polarized flux of the disk (see Sect. 5.3). Image (panel b) is smoothed via a Gaussian kernel with σkernel = 3 px. The isophotal contours show levels of the surface brightness with approximately 25, 40, and 50 counts per binned pixel (from the lowest to the highest contour). Arrows “A” and “B” mark the location of the increased surface brightness, which could indicate the radius of the planetesimal belt. The x-axis coincides with the disk axis at ◦ estimated PA θdisk = 112 (see Sect.5). The color bar shows the surface brightness in counts per binned pixel. and then we determined the difference between the left side r = 0.300 and two small brightness peaks at |x| ≈ 0.300 (8.5 au) and the mirrored right side of the image. The minimum resid- indicated with arrows “A” and “B” in Figs.2b and3. ual flux corresponding to the best match between disk sides Figure3 also includes background profiles determined below ◦ is achieved at θdisk = 113.5 for the data set from 2015-06-26 and above the disk major axis by summing up the counts from (night 177) and at PA = 116.5◦ for the data set from 2015-09-06 y = −0.4200 to y = −0.1300 (light green dotted line) and from (night 249). y = +0.1600 to y = +0.4500 (green solid line). The disk flux ◦ ◦ We adopted the PA equal θdisk = 114 ± 3 . This PA should is at least twice as high as the background, except for a small be corrected for the ZIMPOL True North offset of −2◦, which region around x ≈ +0.2300 where the background is particularly means the preprocessed image must be rotated by 2◦ clockwise. high. The origin of the enhanced background below the disk ◦ ◦ The final PA of the disk is, therefore, θdisk = 112 ± 3 north over midplane is unclear. The errors on flux per bin were calculated east (NoE), where the indicated uncertainty includes associated from the variance of the sum of pixel values in bins assuming systematic errors. For the following data analysis, the Qϕ image a sample of normal random variables. The uncertainty of the was rotated by 24◦ clockwise, including the correction for the pixel value is given by the standard deviation of the flux distri- True North offset, to place the disk major axis horizontally. bution (counts per pixel) computed in concentric annuli in the We introduced an x−y disk coordinate system with the star at Qϕ image (excluding the area containing the disk flux) to take the origin and the +x coordinate along the derived disk major into account the radial dependence of the data variance. As an axis in WNW direction and the y-coordinate perpendicular to additional noise estimator, we measured the background in the ◦ this with the positive axis toward NNE (θ = 22 ) as shown Uϕ image (black solid line in Fig.3) in the same areas where the in Fig.2b. polarized flux of the disk was measured in the Qϕ image. The The observed Qϕ flux image shows areas of enhanced surface polarized scattered light from the disk is detected up to a radial brightness at the separations |x| ' 0.1−0.300 but located about distance of r ∼ 0.800. Beyond r = 0.300, the polarized flux per 0.0400 above the x-axis and this up-down asymmetry is reflected x-bin is less than 8 ct s−1. clearly in the surface brightness contours shown in Fig.2b. Figure3 shows the profile for the polarized flux along the 5.2. Modeling the observed disk flux x-axis measured in bins of ∆x = 29 mas and integrated in the y-direction from y = −0.1300 to y = +0.1600. Our data show We modeled the spatial distribution of dust in HD 172555 a higher flux closer to the star with a maximum flux inside disk with the 3D single scattering code presented in A151, page 5 of 15 A&A proofs: manuscript no. HD172555_final

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c 0.2’’ 6 AU

Fig. 4. Comparison of the grid model with the Qϕ image. Panel a: Q × Panel b Fig. 3. Radial polarized flux profile measured in the Q image per ϕ image after 8 8 binning. : image of the best-fitting grid ϕ Panel c 0.02900(∆x) × 0.29000(∆y) bin (red solid line) compared with profiles of model convolved with the instrumental PSF. : residual image the best-fitting models and background. The background above (green obtained after subtraction of the PSF-convolved grid model image panel b Q panel a solid line) and below (light green dotted line) the disk midplane and ( ) from the ϕ image ( ). Color bar shows flux in counts per binned pixel. the background in the Uϕ image (black solid line) are calculated as explained in Sect.5. The upper limit is set for the polarized flux per bin for the disk regions beyond r = 0.5300. The arrows “A” and “B” point to near side and the inclination higher than 90◦ defines a disk with the surface brightness peaks. its near side toward north as in the case of the HD 172555 disk. To simplify the model computation, we adopt the same grain Engler et al.(2017). The disk geometry is described by a radius properties everywhere in the disk. The average scattering cross r0, where the radial distribution of the grain number density has section per particle is a free parameter included in the scaling a maximum, and by inner and outer radial power-law falloffs factor Ap. with exponents αin and αout, respectively. For the vertical dis- The Qϕ model image is calculated from the combination of tribution, we adopt the simpler Lorentzian profile instead of the the PSF convolved images of the Stokes parameters Q and U. exponential profile. The former profile has already been used for The individual steps of the modeling procedure are described this purpose (e.g., Krist et al. 2005) and has an advantage that it and illustrated in AppendixA. is described with one parameter less. The Lorentzian profile is To find parameters of the model that best fits the Qϕ image given by (Fig.4a), we took a twofold approach: first, we fitted the data with models drawn from a parameter grid and second we used  !2−1  h  the Markov chain Monte Carlo (MCMC) technique. f (h) = a 1 +  , L L H(r)  5.2.1. Grid of models 4 where h is the height above the disk midplane and aL is the peak We define an extensive parameter grid of ∼10 models and number density of grains in the disk midplane. The scale height calculate a synthetic Qϕ image for each model. The explored of the disk H(r) is defined as a half width at half maximum of parameter space and steps of linear sampling are given in the vertical profile at radial distance r and scales as in H(r) = Table2, Cols. 2 and 3. In this first modeling approach, the disk β ◦ H0 (r/r0) . PA is set to θdisk = 112 , which is the PA value found in the pre- The parameters of the model are the PA of the disk θdisk, vious section (Sect. 5.1). The flux scaling factor Ap is treated as the radius of the planetesimal belt r0, inner αin and outer a free parameter for each model and is obtained by minimizing 2 αout power law exponents, scale height H0, flare exponent β, the χ for the fit of the Qϕ model image to the data. The reduced i 2 inclination angle , Henyey–Greenstein (HG) scattering asym- χν metric is estimated as follows: metry parameter gsca, and the scaling factor Ap. The scattering 2 phase function for the polarized flux fp (θ, gsca) is the product N h i 1 Xdata Fi, data − Ap · Fi, model(p) fp (θ, gsca) = HG(θ, gsca) · pRay(θ) of the HG function and the χ2 = , (1) ν ν σ2 Rayleigh scattering function (see Fig. 8 in Engler et al. 2017). i=1 i, data We assume that the debris disk is optically thin and neglect multiple scattering. The HG parameter has only positive values where Ndata is the number of pixels used to fit the data, Fi, data (0 6 gsca 6 1) assuming that the dust particles are predominately is the flux measured in pixel i with an uncertainty σi, data, and forward-scattering as inferred from imaging polarimetry of other Fi, model(p) is the modeled flux of the same pixel. The degree highly inclined debris disks (e.g., Olofsson et al. 2016; Engler of freedom of the fit is denoted by ν = Ndata − Npar, where Npar et al. 2017). This means that the brighter side of the disk is the represents the number of model parameters p = (p1, p2, ..., pNpar ).

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Table 2. Disk model parameters.

Grid model MCMC model Optimized parameter 2 Range Step Min χν Mean value Range Best-ﬁt value

+1.5 Position angle θdisk, deg (...) (...) (...) (...) [109, 114] 112.3−1.5 r +0.06 +1.7 +0.06 +1.7 Radius of “belt” 0, arcsec (au) [0.21, 0.42] 0.0175 0.38 0.36−0.06 10.3−1.7 [0.25, 0.50] 0.40−0.06 11.3−1.7 +0.04 +1.23 +0.01 +0.3 Scale height H0, arcsec (au) [0.00, 0.1] 0.02 0.04 0.05−0.04 1.36−1.23 [0.00, 0.1] 0.02−0.01 0.6−0.3 +3.3 +0.8 Inner radial index αin [0, 6] 1 3 3.5−3.3 [0, 6] 2.3−0.6 − − − +5.7 − − +2.5 Outer radial index αout [ 11, 0] 1 7 6.8−5.7 [ 20, 0] 9.8−4.1 +2.75 +0.4 Flare index β [0.25, 1.50] 0.25 0.25 0.45−2.75 [0.0, 1.0] 0.4−0.3 +8.2 +1.7 Inclination i, deg [96, 111] 1 105 103.5−8.2 [96, 111] 103.8−1.7 +0.38 +0.08 HG parameter gsca [0.2, 1.0] 0.1 0.6 0.64−0.38 [0.2, 1.0] 0.74−0.10 A +12.36 +0.8 Scaling factor p (...) (...) 1.1 0.9−12.36 (...) 2.8−0.9

To be less affected by single pixel noise and to speed up between HG parameter gsca and inclination of the disk i or scale this procedure, we reduce the number of pixels of the original height H0. Qϕ image (Fig.2a) by 8 × 8 binning and select a rectangular image fitting area with a length of 63 and width of 19 binned 5.2.3. Modeling results pixels (1.8300 × 0.5500; Fig.4a) centered on the star. A round area with radius of 2.5 binned pixels covering the coronagraph The MCMC sampling result for the PA of the disk is essentially and a few pixels around this region are excluded from the fitting the same as the PA we found by subtracting one disk side from procedure. the other (Sect. 5.1). Regarding other parameters, the best-fitting 2 The minimum χν = 1.17 is achieved for the model with grid model (Table2, Col. 5) and the MCMC model (Table2, parameters listed in Col. 4 of Table2. Considering all the mod- Col. 7) are consistent with each other. They indicate a disk radius 2 ◦ els that fit the observations well and have a χν < 2, we derive r0 between 10 and 12 au and a disk inclination of ≈103.5 . The the parameter distribution and fit a Gaussian for each model scale height of the vertical profile H0 is 10–20 times smaller parameter (see Fig. C.1). We adopt the mean values of the param- than the radius of the disk. According to the MCMC model, the eter distribution as the best-fitting model presented in Col. 5 of outer density falloff is at least steeper than about αout = −7. It is Table2. The errors on the mean parameters are given by the 68% not clear whether the disk is cleared inside r0 because the inner confidence interval derived for the respective distribution. radial index αin is smaller than 3. Both models indicate a rela- tively high asymmetry parameter for scattering gsca ≈ 0.7. This 5.2.2. MCMC modeling result could be affected by a higher surface brightness, which we observe inside r = 0.200. The flare index β is the only parameter We use the parameters of the best-fitting model from the param- that remains unconstrained in both modeling methods (grid and eter grid (Sect. 5.2.1) as a starting point for the MCMC run. To MCMC) showing a tendency to be 0. perform this analysis, we employed the Python module emcee by Both models fit the Qϕ image equally well according to the Foreman-Mackey et al.(2013), which implements affine invari- 2 2 χν metric: the grid model has a χν = 1.20 (ν = 1152) and the ant MCMC sampler suggested by Goodman & Weare(2010). 2 MCMC model has a χν = 1.19 (ν = 1151). The residual images The uniform priors are defined as specified in Col. 6 of Table2. of both models show no noticeable differences. Therefore, in Contrary to the modeling with a grid of parameters (Sect. 5.2.1), Fig.4, we show only the grid model in comparison to the Qϕ the PA θdisk is allowed to vary. image. For the run of the standard ensemble sampler, 1000 walkers Also, the radial profiles for the polarized flux of both models, are initialized to perform a random walk with 2000 steps. The which are calculated in the same bins as in the Qϕ image posterior distributions of the parameters shown in Fig. C.2 are (Fig.4a), are qualitatively very similar (cf. yellow solid and obtained discarding the burn-in phase of 400 walker steps. The dotted lines in Fig.3). mean fraction of the accepted steps within the chain is 0.342 and the maximum autocorrelation time of parameter samples 5.2.4. Modeling cancellation effect is 90 steps. This indicates a good convergence and stability of the chain by the end of the MCMC run (Foreman-Mackey et al. The synthetic image of the best-fitting model (Fig.4b) is impor- 2013). tant for a correction of the polarized flux due to the extended A set of the most probable parameters, which are consid- instrument PSF. One effect is the loss of polarization signal ered to be the parameters of the best-fitting MCMC model, is because parts of it are outside the flux integration aperture. The listed in Col. 7 of Table2. These parameters are derived as second and more important effect for compact sources is the the 50th percentile of the posterior distribution. Their lower and polarization cancellation effect where the positive and negative upper uncertainties are quoted based on the 16th and 84th per- Q flux features in the Stokes Q image, and similar for Stokes U, centiles of the samples, respectively. Figure C.2 demonstrates the cancel each other substantially if their separation is not much degeneracy between some of the model parameters, for instance, larger than the PSF. As described in Schmid et al.(2006) and A151, page 7 of 15 A&A 618, A151 (2018)

Avenhaus et al.(2014), this can easily cause a reduction of the 5.4. Polarimetric flux measurable polarization flux by a factor of 2 or more, depending on the source geometry and PSF structure. To check our photometry, we compare the measured stellar We determine the total polarized flux for our best-fit model flux with the stellar magnitudes from the literature. The stellar ± × 5 −1 before and after convolution with the instrument PSF and derive count rate of (4.36 0.08) 10 ct s per ZIMPOL arm before for the cancellation effect a factor of 0.61 for our observations correction for the transmission of the neutral density filter can be of the HD 172555 debris disk. In addition, we find that only converted to the photometric magnitude m(VBB) (Schmid et al. 82% of the polarized flux of the convolved images fall into 2017) as follows: the rectangular disk-flux measuring areas indicated by the white − −1 − · − corners in Fig.2a, while 4% of the flux is covered by the coro- m(VBB) = 2.5 log(ct s ) am k1(VBB) mmode +zpima(VBB), nagraphic mask near the star and 14% of the polarized flux m where am = 1.3 is the airmass, k1(VBB) = 0.086 is the filter are distributed in a very low surface brightness halo further m out. coefficient for the atmospheric extinction, zpima(VBB) = 24.61 is the photometric zero point for the VBB filter, and mmode = 5.64m is an offset to the zero point, which accounts for the 5.3. Measured polarized flux contrast of the disk instrument configuration, pupil stop (STOP1_2), neutral density filter ND2.0, and the fast polarimetry detector mode. For To compare the polarized flux from the disk with the stellar flux, m m we first derive the expected count rates of the star in the coro- HD 172555, we derive a magnitude m(VBB) = 4.68 ± 0.03 nagraphic image if there were no coronagraph hiding its PSF (indicated with a black asterisk in Fig.5). This value is in good R peak. This is obtained with the flux frames where the star is off- agreement with the Johnson photometric magnitude in band m . m ± . m I m = . m ± . m set from the coronagraphic mask. We use two flux measurements (R) = 4 887 0 023 and band (I) 4 581 0 025 from the nights when we obtained good results (177 and 249) and (Johnson et al. 1966). derive a mean count rate for the central star of (4.36 ± 0.08) × 105 For the estimated above ratio of the disk total polarized flux F /F . ± . × −5 counts per second (ct s−1) per ZIMPOL arm by summing up to stellar flux ( pol)disk ∗ > (6 2 0 6) 10 , disk magnitude mp m± m all counts registered within the aperture with a radius of 1.500 in the VBB filter is disk(VBB) = 15.20 0.37 (indicated (413 pixels). Then we correct with a factor of 1.007 for the coro- with a blue asterisk in Fig.5). r ≈ . 00 nagraph attenuation at a distance of 0.3500 from the stellar PSF At radial separation of 0 3 indicated with arrows “A” peak and a factor of ∼115 to account for the mean transmission and “B” in Figs.2b and3, the peak surface brightness is ∼15 ct s−1 per binned pixel (0.02900 × 0.02900) and corresponds to of the neutral density filter ND2.0 in the VBB filter. We obtain m m −2 − = . ± . an average count rate of (5.00 ± 0.14) × 107 ct s 1 per ZIMPOL the SBpeak(VBB) 13 3 0 3 arcsec or surface brightness contrast for the polarized flux of SBpeak(VBB) − mstar(VBB) = arm for the expected flux of the central star for observation −2 in the fast polarimetry mode with the pupil mask but without 8.62 mag arcsec . correction for the attenuation by the focal plane mask or ND2.0 filter. 6. Discussion For the disk, we derive the total polarized flux by summing up all the counts in two rectangular areas indicated with white 6.1. Comparison with thermal light detection and brackets in Fig.2a, from |x| = 0.0800 to 0.7700 along the major interferometry axis and from y = −0.1300 to 0.1600 perpendicular to it. The 00 The disk geometry is consistent with the 18 µm image presented innermost regions with radial separations |x| < 0.08 are largely in Smith et al.(2012). They found two lobes of extended hidden behind the coronagraphic mask, and therefore they are emission along PA = 110◦ with a separation of about 0.400 from not included in this estimate. The total polarized flux in the the star and a flux of 105 mJy. On top of this, they measured a VBB filter after the modulation–demodulation efficiency cali- roughly seven times stronger (732 mJy) unresolved dust compo- bration amounts to 780 ± 150 (ESE side, left) and 760 ± 150 N −1 nent and a stellar flux of 202 mJy. In the -band image the dust (WNW side, right) ct s and per ZIMPOL arm. Therefore, the was not resolved by Smith et al.(2012), but their N-band MIDI total net flux obtained by integrating over abovementioned areas −1 interferometry resolved the dust fully, putting it at separations is 1540 ± 300 ct s per ZIMPOL arm. between >0.03500 and <0.2700 (1 − 8 au). Therefore, we also This measured flux must still be corrected for the polarimet- expect that a lot of polarized light from the dust scattering ric cancellation effects to get a value for the intrinsic polarized contributes to the signal inside the inner working angle of the flux. Because of the limited spatial resolution of our data, the SPHERE/ZIMPOL observations at 0.1200, which cannot be polarization in the positive and negative Q regions is reduced measured. since signals with opposite signs overlap and cancel each other. The disk modeling of the infrared flux by Smith et al.(2012) We quantified this effect and calculated correction factors using yields a disk with radius r = 0.2700 and width dr = 1.2r, which is our best-fit model (see description in the last paragraph of equivalent to the ring with constant surface brightness between Sect. 5.2). 0.100 and 0.400, inclined at 75◦ to the line of sight and at PA = Taking into account the PDI efficiency, which causes the 120◦ for the disk major axis. We confirm these parameters with reduction of disk polarized flux by a factor of ∼1.7 and correc- our observation and can provide more stringent parameters for tion factor for the aperture size (see Sect. 5.2), the total polarized the inclination and the disk orientation because of the higher flux of the disk is at least twice as large as the total net flux and −1 spatial resolution of our data. Also the disk extension agrees, but is equal to 3100 ± 600 ct s per ZIMPOL arm. This flux corre- it is not clear whether the scattered light emission and thermal sponds to the intrinsic modeled polarized flux compatible with emission should show the same radial flux distributions. our observation. With this value, the lower limit for the ratio of In Fig.5, we compare the flux distribution λFλ from the the disk total polarized flux to the stellar flux is (Fpol)disk/F∗ > stellar photosphere with the thermal emission of the disk and −5 −5 (6.2 ± 0.6) × 10 (cf. with the ratio (Fpol)disk/F∗ = 3.1 × 10 the polarized flux distribution measured in this work. Photomet- −1 obtained for the net flux (Fpol)disk = 1540 ct s ). ric data points of HD 172555 are listed in Table3 and plotted A151, page 8 of 15 N. Engler et al.: HD 172555 hot debris disk

Fig. 5. Photometry of the star and disk together with the blackbody SED ﬁts.

Table 3. Photometry of HD 172555. blue dotted line shows an approximate curve for the SED of the polarized light obtained by scaling down the SED of the star. Using our best-fitting grid model, we roughly estimated the scat- Filter Wavelength Flux density Error Ref. tered flux from the disk (averaged over full solid angle) in the (µm) (Jy) (Jy) VBB filter. This conversion neglects the contribution from the Johnson B 0.44 53.87 0.94 1 diffracted light and assumes that the maximum polarization frac- p = . Johnson V 0.55 38.45 0.53 1 tion of the phase function for the polarized flux is max 0 3. This value is denoted with a yellow asterisk and labeled hIscai. Johnson R 0.7 33.40 0.71 1 We used this magnitude as a proxy for the scattered flux of the Johnson I 0.9 35.74 0.82 1 disk to compare it with the maximum thermal flux of the disk at λ = 10 µm and thus to estimate a kind of the disk albedo. N Si-5 ( ) 11.7 1.120 0.067 2 We obtain hIscai (pmax = 0.3)/λFλ (λ = 10 µm) = 0.54, which Qa (Q) 18.3 1.039 0.085 2 should be considered as a very rough estimate for this ratio. The lower and upper limits on the scattered flux Isca, shown in PACS70 70 0.191 0.005 3 Fig.5, are obtained assuming maximum polarization fraction PACS100 100 0.089 0.003 3 pmax = 0.1 (for the upper limit) and pmax = 0.7 (for the lower limit). PACS160 160 0.036 0.02 3 6.2. Hidden source of thermal emission References. (1) Johnson et al.(1966); (2) Smith et al.(2012); (3) Riviere-Marichalar et al.(2012). According to the mid-IR observations of Smith et al.(2012), most of the dust is located inside 8 au, down to 1 au. There- as green diamonds in Fig.5, which also includes a Spitzer/IRS fore, we investigate with model calculations whether a strong but spectrum1. The stellar spectral flux density is approximated compact source of scattered light could be present, which is not by a Planck function for the star temperature of 7800 K detectable in our data because of the limited resolution and inner (Riviere-Marichalar et al. 2012). A black asterisk (labeled VBB) working angle limit of the used coronagraph. denotes the stellar magnitude measured in the VBB (this work). The occulting spot in our coronagraphic data has a radius r ∼ 0.0800 (2.27 au). We model a small disk with a radius of 2 au The near-IR aperture photometry of HD 172555 in the N and 00 Q bands (green diamonds at 11.7 and 18.3 µm), performed by (0.07 ) with exactly the same geometric morphology as the best- Smith et al.(2012) using TReCS imaging data, is indicated by fit grid model derived in Sect 5.2, but just smaller by a factor of capital letters N and Q. The thermal flux from the disk is shown 5. This small disk is shown als Qϕ image in Fig.6a, together with as a blackbody emission with the temperature of 329 K found the convolved Qϕ image with the size of the coronagraphic mask by Riviere-Marichalar et al.(2012; orange solid line). The net indicated in Fig.6b. First, we notice a large difference between Q intrinsic polarized flux and the convolved polarized flux of polarized flux measured in the Qϕ image (Sect. 5.3) is indicated ϕ a factor of 2.5 because of the very strong polarimetric cancella- by a light blue asterisk (labeled with Ipol = Qϕ), and the polarized flux corrected for the polarimetric cancellation effects and tion for such a compact disk. Then, there is another factor 2.67 aperture size is indicated by a blue asterisk in this figure. The between the total convolved polarized flux from the disk and the convolved polarized flux that falls into the rectangular measur- 1 http://www.stsci.edu/cchen/irsdebris.html ing areas of our observations shown in Fig.2a because a major

A151, page 9 of 15 A&A 618, A151 (2018)

N E

0.1 ’’

1 4 7 10 -0.5 0.5 1.5 2.5 -0.8 -0.4 0 0.4 0.8

Fig. 6. Model of the small debris disk that could be hidden behind the coronagraphic mask. The model parameters correspond to those of the mean model (Table2) except the radius of the belt and scale height of the dust vertical distribution, which are reduced by a factor of 5. Panel a: Qϕ image of the debris disk model showing the polarized intensity before being convolved with the instrumental PSF. Panel b: Qϕ image of the debris disk model showing the polarized intensity after convolution with the instrumental PSF. The black circle denotes the edge of the coronagraphic mask. Panel c: Uϕ image of the model demonstrating nonzero Uϕ signal appearing after convolution of the Stokes Q and U parameters with the instrumental PSF. The color bars show counts per pixel. region of the polarization signal is hidden by the coronagraphic or disk with a radius in the range between 0.300 (8.5 au) and mask. Thus, only about 15 % of the polarized flux produced by 0.400 (11.3 au). We analysed the disk structure and obtained the an inner compact disk would contribute to our measurement. We following results: −1 ◦ ◦ measure a net flux of 1540 ct s in the measuring area of our – The PA for the disk major axis is θdisk = 112.3 ± 1.5 on the observation and estimate that it is not possible to recognize an sky. inner disk in our data, which contributes less than 150 ct s−1 – The disk emission is slightly shifted in NNE direction to our measurement. Thus, an unseen compact disk with the from the star indicating that the front side or forward- geometry as described above and an intrinsic polarized flux of scattering part of the disk is on the NNE side. The observed 6.675 × 150 ct s−1 could be present without being in conflict with dust distribution can be described with the HG asymmetry our observations and even more scattered light could be hidden parameter g ≈ 0.7 and disk inclination ≈103.5◦. for a more compact inner disk. – Data analysis and modeling results do not suggest the clear- ing of the inner disk regions (inside r = 0.300). – The total disk magnitude in polarized flux in the VBB 6.3. Comparison between polarized flux and m m thermal emission filter is mpdisk(VBB) = 15.20 ± 0.37 and the stellar flux is m(VBB) = 4.68m ± 0.03m. This gives a disk to −5 To characterize the scattering albedo of the dust, we compute the star contrast (Fpol)disk/F∗ of (6.2 ± 0.6) × 10 . The mea- Λ parameter describing the ratio of the fractional polarized light sured peak surface brightness of the polarized light is m m −2 flux to fractional infrared luminosity excess of the disk (Engler SBpeak(VBB) = 13.3 ± 0.3 arcsec . This corresponds to a et al. 2017), i.e., surface brightness contrast of SBpeak(VBB) − mstar(VBB) = 8.62 mag arcsec−2. (F ) /F∗ Λ = pol disk , – When compared with the fractional infrared luminosity of LIR/L∗ the disk using the Λ parameter, the fractional polarized light flux in the VBB filter makes up ∼9%. where the ratio of total polarized flux of the disk to the stellar flux Our data demonstrate high sensitivity and ability of ZIMPOL to ± × −5 for HD 172555 is (Fpol)disk/F∗ > (6.2 0.6) 10 (Sect. 5.3). resolve the polarized light from the hot debris around a nearby Adopting the ratio of the disk infrared luminosity to stellar lumi- A star as close as 0.100 or ∼3 au. It would be worth reobserving × −4 nosity LIR/L∗ equal to 7.2 10 (Mittal et al. 2015), we obtain a HD 172555 in the I band without the coronagraph. Additional lower limit for Λ > 0.086. This value is slightly smaller than the observations of this target under excellent observing conditions, Λ parameters we have estimated for the F star HIP 79977 and the i.e., seeing 60.7, airmass 61.4, coherence time >3.5 ms, and M star AU Mic (ΛHIP 79977 = 0.11 and ΛAU Mic = 0.55) in Engler wind speed >3 m s−1, to avoid the low wind effect (see SPHERE et al.(2017). Manual) and with different offsets of the sky field on the detector would allow us to better distinguish between the instrumental 7. Summary features in the PSF and the real astrophysical signal. In the VBB filter, the speckle ring extends from 0.3000 to 0.4500 and over- In this paper, we presented images of polarized scattered light laps the region of interest. In the I band, the speckle ring is from the debris disk around HD 172555 obtained in the VBB further outside of ∼0.4000 and the achievable contrast is higher filter using differential polarimetry. We found that the observed under optimal observing conditions even if the amount of pho- polarized intensity is consistent with an axisymmetric dust distri- tons received in the I band is a factor of 0.6 lower than in the bution, which can be interpreted as a parent belt of planetesimals VBB. Moreover, noncoronagraphic data taken with I band are

A151, page 10 of 15 N. Engler et al.: HD 172555 hot debris disk more suitable for the measurement of the beam shift between the Gray, R. O., Corbally, C. J., Garrison, R. F., et al. 2006, AJ, 132, 161 two orthogonal polarization states and, hence, the correction of Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27 the beamshift effect (Schmid et al. 2018) is much easier. Such Johnson, H. L., Mitchell, R. I., Iriarte, B., & Wisniewski, W. Z. 1966, Commu- nications of the Lunar and Planetary Laboratory, 4, 99 observation may also allow us to probe the innermost dust in the Johnson, B. C., Lisse, C. M., Chen, C. H., et al. 2012, ApJ, 761, 45 HD 172555 system. Kasper, M., Beuzit, J.-L., Feldt, M., et al. 2012, Messenger, 149, 17 Kiefer, F., Lecavelier des Etangs, A., Augereau, J.-C., et al. 2014, A&A, 561, L10 Acknowledgements. We would like to thank the referee for many thoughtful com- Krist, J. E., Ardila, D. R., Golimowski, D. A., et al. 2005, AJ, 129, 1008 ments that helped to improve this paper. This work is supported by the Swiss Lisse, C. M., Chen, C. H., Wyatt, M. C., et al. 2009, ApJ, 701, 2019 National Science Foundation through grant No. 200020 – 162630. Maire, A.-L., Langlois, M., Dohlen, K., et al. 2016, in Ground-based and Airborne Instrumentation for Astronomy VI, Proc. SPIE, 9908, 990834 Mamajek, E. E., & Bell, C. P. M. 2014, MNRAS, 445, 2169 References Matthews, B. C., Krivov, A. V., Wyatt, M. C., Bryden, G., & Eiroa, C. 2014, Protostars and Planets VI, 521 Avenhaus, H., Quanz, S. P., Meyer, M. R., et al. 2014, ApJ, 790, 56 Mittal, T., Chen, C. H., Jang-Condell, H., et al. 2015, ApJ, 798, 87 Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, in Ground-based and Airborne Moerchen, M. M., Telesco, C. M., & Packham, C. 2010, ApJ, 723, 1418 Instrumentation for Astronomy II, Proc. SPIE, 7014, 701418 Moór, A., Ábrahám, P., Derekas, A., et al. 2006, ApJ, 644, 525 Bonnefoy, M., Milli, J., Ménard, F., et al. 2017, A&A, 597, L7 Morales, F. Y., Rieke, G. H., Werner, M. W., et al. 2011, ApJ, 730, L29 Chen, C. H., Sargent, B. A., Bohac, C., et al. 2006, ApJS, 166, 351 Olofsson, J., Samland, M., Avenhaus, H., et al. 2016, A&A, 591, A108 Chen, C. H., Mamajek, E. E., Bitner, M. A., et al. 2011, ApJ, 738, 122 Quanz, S. P., Kenworthy, M. A., Meyer, M. R., Girard, J. H. V., & Kasper, M. Choquet, É., Perrin, M. D., Chen, C. H., et al. 2016, ApJ, 817, L2 2011, ApJ, 736, L32 Cote, J. 1987, A&A, 181, 77 Riviere-Marichalar, P., Barrado, D., Augereau, J.-C., et al. 2012, A&A, 546, L8 Dohlen, K., Beuzit, J.-L., Feldt, M., et al. 2006, Proc. SPIE, 6269, 62690Q Schmid, H. M., Joos, F., & Tschan, D. 2006, A&A, 452, 657 Engler, N., Schmid, H. M., Thalmann, C., et al. 2017, A&A, 607, A90 Schmid, H. M., Bazzon, A., Milli, J., et al. 2017, A&A, 602, A53 Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, Schmid, H. M., Bazzon, A., Roelfsema, R., et al. 2018, A&A 306 DOI: 10.1051/0004-6361/201833620 Fujiwara, H., Ishihara, D., Kataza, H., et al. 2009, in AKARI, a Light to Illu- Schneider, G., Grady, C. A., Hines, D. C., et al. 2014, AJ, 148, 59 minate the Misty Universe, ed. T. Onaka, G. J. White, T. Nakagawa, & Schütz, O., Meeus, G., & Sterzik, M. F. 2005, A&A, 431, 175 I. Yamamura, Astronomical Society of the Paciﬁc Conference Series, 418, Smith, R., Wyatt, M. C., & Haniff, C. A. 2012, MNRAS, 422, 2560 109 Torres, C. A. O., Quast, G. R., da Silva, L., et al. 2006, A&A, 460, 695 Fusco, T., Sauvage, J.-F., Petit, C., et al. 2014, in Adaptive Optics Systems IV, Trilling, D. E., Bryden, G., Beichman, C. A., et al. 2008, ApJ, 674, 1086 Proc. SPIE, 9148, 91481U Wilson, T. L., Nilsson, R., Chen, C. H., et al. 2016, ApJ, 826, 165 Gaia Collaboration 2016, VizieR Online Data Catalog, 1337 Wyatt, M. C. 2008, ARA&A, 46, 339 Goodman, J., & Weare, J. 2010, Comm. App. Math. Comp. Sci., 5, 65 Wyatt, M. C., Smith, R., Greaves, J. S., et al. 2007a, ApJ, 658, 569 Grady, C. A., Brown, A., Welsh, B., et al. 2018, AJ, 155, 242 Wyatt, M. C., Smith, R., Su, K. Y. L., et al. 2007b, ApJ, 663, 365

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Appendix A: Modeling the Qϕ and Uϕ images

a c e g + U N + E Q Q-

U- W S

b d f h

Fig. A.1. Model images of the polarized flux from HD 172555 debris disk. Images were generated using the parameters of mean model (Col. 5 in Table2) and illustrate the individual steps of the modeling procedure ( from left to the right panels) to obtain the final synthetic Qϕ and Uϕ images (panels g and h). For a detailed description of the presented images, see AppendixA. The diagram on the right side of the figure explains orientation of the axes used to measure the Stokes Q and U parameters as implemented in ZIMPOL instrument. The diagram shows also the orientation of north and east in each image. The north is rotated by 22◦ clockwise from the vertical line to have disk axis in horzontal position. Nonalignment of the disk axes with the Q and U measuring axes causes asymmetric flux distribution in Q and U images (panels c–f).

Figure A.1 simulates the polarized flux measurement with the the ZIMPOL data reduction pipeline. Usually they are used to ZIMPOL instrument. In the first step, the distribution of the dust compute the final Qϕ and Uϕ images of the disk applying reverse number density in the disk is generated using the parameters coordinate transformation as follows: of the mean model. Then, synthetic images of debris disk in Qϕ = −(Q cos 2ϕ + U sin 2ϕ), (A.3) polarized light are calculated assuming only the single scattering Uϕ = −Q sin 2ϕ + U cos 2ϕ. (A.4) of photons. An image of the polarized imtensity, or Qϕ image

(Fig. A.1a), is obtained considering angular dependence of Examination of the final Qϕ and Uϕ images (Fig. A.1g and h) polarization fraction on scattering angle θ such as that for leads to two important conclusions. Comparison of the uncon- Rayleigh scattering. Single scattering of photons produces volved and convolved Qϕ images (Fig. A.1a and g) demonstrates linearly polarized light oriented perpendicular to the scattering the loss of a fraction of the polarized flux due to the convolu- plane, which corresponds to the azimuthal orientation of electric tion of the intensity of two orthogonal polarization states with field in the 2D Qϕ image. The Uϕ image (Fig. A.1b) displays the instrumental PSF (see also Sect. 5.2). As a result of blurring no signal because the Stokes Uϕ parameter should show the ◦ effect on the positive and negative signals in the Stokes Q and polarization component in direction at 45 to the azimuthal U due to the convolution with PSF, a nonzero signal is present direction. In this direction we do not expect to measure any in the final Uϕ image (Fig. A.1h). For the mean model shown in signal if the assumption of single scattering is valid. Fig. A.1, the generated Uϕ flux is of one order smaller than the Q U In the following step, the Stokes and images are Qϕ flux that we measure in the Qϕ image (Fig. A.1g). In general, calculated using the coordinate transformation: this artificially created Uϕ flux and the magnitude of the flux loss Q = −Qϕ cos 2ϕ, (A.1) in the Qϕ image depend on the geometry and extent of the polarized flux source and on the PSF structure. For the small compact U = −Qϕ sin 2ϕ, (A.2) sources, the generated Uϕ flux and the PDI efficiency loss are the where ϕ is the polar angle of each image point and is mea- largest because the resolution of instrument is limited. There- sured from NoE. This polar coordinate system corresponds to fore, this effect should be estimated by means of modeling for the measurement axes of the instrument shown on the right side each individual object and detector. To demonstrate this point, of Fig. A.1. In ZIMPOL, the Stokes Q+ parameter is measured we calculate two additional models with the same parameters along north-south axis and the Stokes U+ parameter is measured and the same aspect ratio of radius of the planetesimal belt to along northeast-southwest axis. scale height as in the mean model but with different radii of the The Q and U images (Fig. A.1c and d) are employed to cre- belts: one model with radius r = 2 au (0.0700) shown in Fig.6 00 ate the images of individual polarization states I0, I45, I90, and and another model with the radius r = 30 au (1.05 ). Our results I135. These images are firstly convolved with the PSF measured show that the total polarized flux of the smaller debris disk is from the HD 172555 data and then are utilized to calculate new reduced by a factor of 0.4, whereas the extended disk suffers images of the Q and U parameters again but now in convolved much less from the convolution effect and reducing factor is 0.73 state (Fig. A.1e and f). These two images imitate the output of for this disk. A151, page 12 of 15 N. Engler et al.: HD 172555 hot debris disk

Appendix B: HD 172555 polarimetric data per (Stokes I) and Stokes parameters Q and U of the data presented observing run in rows two and four in this ﬁgure are also available in electronic form at the CDS. Figure B.1 shows the reduced imaging data of HD 172555 from all six observing runs. The FITS ﬁles of the total intensity

Fig. B.1. Reduced imaging data of HD 172555 from all six observing runs arranged from top to the bottom with the Stokes I (left column), Q (middle column) and U (right column) data. Each run was carried out with ﬁxed sky orientation on the CCD detector with PA offset indicated in parenthesis. The highest quality observations are in rows two and four. To get north up and east to the left, each - arcsec image should be rotated by the PA offset counterclockwise - Stokes I flux (ct) Stokes Q / U flux (ct) and the True North offset of the ZIMPOL should be taken into account. The yellow lines in the Q and U images show the position of disk major axis.

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Appendix C: Probability distributions for ﬁtted parameters See Figs. C.1 and C.2.

2 Fig. C.1. One-dimensional marginalized distributions of model parameters drawn from the sample of well-ﬁtting models (χν < 2). The red dotted lines denote Gaussian ﬁts to the parameter distributions. Their mean values µ and standard deviation σ are given in brackets.

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Fig. C.2. One- and two-dimensional posterior probability distributions of the ﬁtted parameters.

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